Abstract

The quantum dynamics of a two-level system illuminated by a few-cycle pulse with an adjustable carrier-envelope (C-E) phase is investigated theoretically. We consider the weak-field regime where tunneling processes and multiphoton ionization are negligible. It is shown that the upper state population exhibits a strong dependence on the C-E phase and on the time of arrival of the few-cycle pulse if the system is initially prepared in a coherent superposition state. We demonstrate that this effect can be employed to probe the coherence properties of the superposition state and allows one to determine the phase of the laser that prepares this state.

Figures (5)

Two-level system with ground |0⟩ and excited |1⟩ states interacting with two laser pulses that arrive at times TL and TFC, respectively. In step I, a π/2 pulse with Rabi frequency ΩL creates a coherent superposition state. This state is probed in step II by a few-cycle pulse with Rabi frequency ΩFC and C-E phase ϕCE. Note that the duration of the pulses and the time lag between them are not drawn to scale.

Population of the excited state |1⟩ versus the laser phase ϕL and the phase ϕFC [see Eq. (10)] after the interaction with the two pulses shown in Fig. 1. We set ϕD=0, since the dipole phase does not influence the population dynamics. The parameters are Ω0=0.04ω0 and τ=14/ω0.

Comparison of the upper state population without [see Eq. (12)] and with [see Eq. (15)] rotation-wave approximation. The population of the excited state |1⟩ versus the laser phase ϕL for ϕFC=0 and a pulse area of a=∫−∞∞dt′ΩFC(t′)=πΩ0τ=1. Other parameters are the same as Fig. 3. For the chosen pulse area, the rotating-wave approximation is thus a good approximation even when the few-cycle pulse includes half a wave cycle. For the Gaussian pulse defined in Eq. (7), the full width at half-maximum (FWHM) of the pulse intensity envelope is Tenv=(4
ln
2)τ. The cycle number then is Nenv=Tenv/(2π/ω0)=(4
ln
2)τω0/(2π). For τ=1.5/ω0, we have Nenv=0.4.

Measurement of the population in the excited state. The laser ΩP is applied to transfer the excited state population into the third auxiliary state |2⟩. The population in the excited state |1⟩ can be determined by monitoring the fluorescence light emitted from state |2⟩.